A semicircle is developed when a lining passing with the center touches the two ends top top the circle.
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In the below figure, the line AC is dubbed the diameter that the circle. The diameter divides the circle right into two halves such that they space equal in area. These two halves are referred to as the semicircles. The area the a semicircle is half of the area of a circle.
A one is a locus of points equidistant native a given suggest which is the center of the circle. The common distance native the center of a circle to its point is dubbed a radius.
Thus, the circle is entirely characterized by its center (O) and also radius (r).
Area of Semi Circle
The area of a semicircle is fifty percent of the area of the circle. Together the area the a one is πr2. So, the area the a semicircle is 1/2(πr2 ), whereby r is the radius. The value of π is 3.14 or 22/7.
Area that Semicircle = 1/2 (π r2) |
Perimeter the Semicircle
The perimeter of a semicircle is the sum of the fifty percent of the circumference of the circle and diameter. Together the perimeter the a one is 2πr or πd. So, the perimeter of a semicircle is 1/2 (πd) + d or πr + 2r, where r is the radius.
Therefore,
The perimeter that Semicircle = (1/2) π d + d Or Circumference = (πr + 2r) |
Semi one Shape
When a one is cut into 2 halves or when the one of a circle is split by 2, we gain semicircular shape.
Since semicircle is fifty percent that that a circle, thus the area will be half that of a circle.
The area that a one is the number of square systems inside the circle.
Let united state generate the above figure. This polygon have the right to be broken into n isosceles triangle (equal sides gift radius).
Thus, one such isosceles triangle have the right to be represented as displayed below.
The area that this triangle is provided as ½(h*s)
Now for n variety of polygons, the area that a polygon is provided as
½(n*h*s)
The term n × s is equal to the perimeter the the polygon. As the polygon gets to look more and more like a circle, the value philosophies the circle circumference, which is 2 × π × r. So, substituting 2×π×r for n × s.
Polygon area = h/2(2 × π × r)
Also, as the number of sides increases, the triangle it s okay narrower and so as soon as s philosophies zero, h and r have actually the very same length. For this reason substituting r because that h:
Polygon area = h/2(2 × π × r)
= (2 × r × r × π)/2
Rearranging this us get
Area = πr2
Now the area of a semicircle is equal to fifty percent of that of a complete circle.
Therefore,
Area that a semicircle =(πr2)/2
Semi one Formula
The listed below table reflects the formulas linked with the semicircle that radius r.
Area | (πr2)/2 |
Perimeter (Circumference) | (½)πd + d; as soon as diameter (d) is known |
πr + 2r | |
Angle in a semicircle | 90 degrees, i.e. Appropriate angle |
Central angle | 180 degrees |
Semi circle Examples
Example 1:
Find the area the a semicircle of radius 28 cm.
Solution:
Given,
Radius that semi one = r = 28 cm
Area the semi circle = (πr2)/2
= (½) × (22/7) × 28 × 28
= 1232
Therefore, the area the the semi one is 1232 sq.cm.
Example 2:
What is the perimeter of a semicircle through diameter 7 cm?
Solution:
Given,
Diameter that semicircle = d = 7 cm
Formula because that the circumference (perimeter) that a semicircle utilizing its diameter = (½)πd + d
Substitute the value of d, us get;
= (½) × (22/7) × 7 + 7
= 11 + 7
= 18
Therefore, the perimeter that the semicircle is 18 cm.
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Frequently Asked inquiries on Semicircle
Is a semicircle fifty percent the circle?
Yes, a semicircle is half the circle. That means, a circle can be separated into two semicircles.